BSTAT 2305 test 2

A random sample of size 100 is taken from a population described by the proportion p=0.60. what are the expected value and the standard error for the sampling distribution of the sample proportion?

0.600 and 0.049

The probability P(Z < 1.28) is closest to ______.

0.90

Find the probability P(−1.80 ≤ Z ≤ 1.80).

0.9282

Find the probability P(−1.90 ≤ Z ≤ 1.90).

0.9426

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. Given a sample of nine electricians, what is the standard deviation for the sampling distribution of the sample mean?

4,000

The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that of -0.90.

False

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)?

P(X > 16) is greater than P(X < 16).

It is known that the length of a certain product X is normally distributed with μ = 15 inches. How is the probability P(X > 16) related to P(X < 16)?

P(X > 16) is smaller than P(X < 16).

Assume the sample space S = {win, loss}. Select the choice that fulfills the requirements of the definition of probability.

P({win}) = 0.4 P({loss}) = 0.6

The covariance can be use to determine the strength of a linear relationship between two variables.

True

The deterministic component of a linear regression model is due to the omission of relevant factors that influence the response variable.

True

The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.

True

The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to ten.

True

A sample regression equation is given by = −100 + 0.5x. If x = 20, the value of y is ________.

Unknown

We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?

[11.7019, 13.2981]

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At the 5% significance level, the decision is to ___________.

do not reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800

Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n)

estimate

For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level 100(1-σ)%

false

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error or bound on error is B = 1.5? The population standard deviation is known to be 10.75.

n = 198

If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α = 0.05, then the correct conclusion is to ____________________.

not reject the null hypothesis

The following scatterplot indicates that the relationship between the two variables x and y is ________.

strong and positive

The correlation coefficient can only range between 0 and 1.

False

The covariance and correlation coefficient are measures that quantify the non-linear relationship between two variables.

False

Find the z value such that P(Z ≤ z) = 0.9082.

z = 1.33

Find the z value such that P(Z ≤ z) = 0.9099.

z = 1.34

If the random variable X is normally distributed with a mean of 55 and a standard deviation of 4, then P(X >55) is:

0.5

The sample correlation coefficient cannot equal zero.

False

Consider the following hypotheses: H0: p ≥ 0.38 HA: p < 0.38 Compute the p-value based on the following sample information. x= 110; n = 300

.3192

The probability P(Z =1.28) is closest to ______.

0.00

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______.

0.0957

Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price?

0.24

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. under 30 30+ yes 76 65 no 24 35 The probability that a respondent is at least 30 years old is the closest to ______.

0.33

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

150

What is for a 95% confidence interval of the population mean based on a sample of 25 observations?

2.064

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event Ac and what is the probability of this event?

Ac = {TTT, HHT, HTH, THH, HHH}; P(Ac) = 0.625

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

Do not reject Ho; we cannot conclude that the mean differs from zero.

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

False

A residual is the difference between the predicted and observed values of y.

False

For a given confidence level 100(1-σ)% and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size.

False

For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level

False

The following scatterplot indicates that the relationship between the two variables x and y is ________.

Strong and negative

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?

t15 = -3.00

Find the z value such that P(Z ≤ z) = 0.9066.

z = 1.32

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________.

the franchiser builds on an unacceptable site